This two-day event aims to connect women graduate students and beginning researchers with more established female researchers who use optimal transportation in their work and can serve as professional contacts and potential role-models. As such, it will showcase a selection of lectures featuring female scientists, both established leaders and emerging researchers.
These lectures will be interspersed with networking and social events such as lunch or tea-time discussions led by successful researchers about (a) the particular opportunities and challenges facing women in science---including practical topics such as work-life balance and choosing a mentor, and (b) promising new directions in optimal transportation and related topics. Junior participants will be paired with more senior researchers in mentoring groups, and all participants will be encouraged to stay for the Introductory Workshop the following week, where they will have the opportunity to propose a short research communication.
Accommodation:
A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.
A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.
MSRI has a preferred rate of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. There is no cut-off date for reservations. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and enter dates of stay at top of screen and click Book Now. Once on the reservation page, click "Preferred/Corporate Rate Accounts" and input the code: msri.

This two-day event aims to connect women graduate students and beginning researchers with more established female researchers who use optimal transportation in their work and can serve as professional contacts and potential role-models. As such, it will showcase a selection of lectures featuring female scientists, both established leaders and emerging researchers.

These lectures will be interspersed with networking and social events such as lunch or tea-time discussions led by successful researchers about (a) the particular opportunities and challenges facing women in science---including practical topics such as work-life balance and choosing a mentor, and (b) promising new directions in optimal transportation and related topics.Junior participants will be paired with more senior researchers in mentoring groups, and all participants will be encouraged to stay for the Introductory Workshop the following week, where they will have the opportunity to propose a short research communication.

Accommodation:

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

MSRI has a preferred rate of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. There is no cut-off date for reservations. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and enter dates of stay at top of screen and click Book Now. Once on the reservation page, click "Preferred/Corporate Rate Accounts" and input the code: msri.

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

Recent advances in Geometric Analysis and in Optimal Transport have provided new insight into both fields. In Geometric Analysis we study the limits of sequences of Riemannian manifolds and produce limit spaces with a variety of structures. With lower bounds on Ricci curvature, Cheeger-Colding combined Gromov's Compactness Theorem and ideas of Fukaya to show that sequences of Riemannian manifolds with uniform lower Ricci curvature bounds have metric measure limits. They show these limits are metric measure spaces with a doubling measure that has many of the properties of a Riemannian manifold with a lower Ricci curvature bound. Sturm and Lott-Villani then generalized the notion of a lower Ricci curvature bound to metric measure spaces using notions from Optimal Transport. Sturm also defined a new notion of metric measure convergence of metric measure spaces based upon the Optimal Transport notion of a Wasserstein distance between probability measures.
Other notions of convergence provide more structure on the limit spaces and do not require the lower Ricci curvature bound. One notion, with applications in General Relativity, is the intrinsic flat distance introduced in joint work with Stefan Wenger (building upon work of Ambrosio-Kirchheim) produces integer weighted countably $\mathcal{H}^m$ rectifiable limit spaces. A newer notion soon to be introduced in joint work with Guofang Wei (building upon work of Solorzano and on Sturm's metric measure convergence) preserves the structure of the tangent bundle. We provide a brief survey of these notions with examples. The details in the papers can be understood after the audience has attended the introductory workshop next week.

" Higher order isoperimetric inequalities --an approach via the method of
optimal transport."
One of the method to derive sharp isoperimetric inequality for domains
in the Euclidean is to apply the method of optimal transport; in this
talk, I will report some recent joint work with Yi Wang to extend the method
to prove some higher order isoperimetric inequalities with
integrands involving symmetric functions of the second fundamental form.

The purpose of this talk is to present an overview of the applications of optimal transport in computer vision, image and video processing. The use of optimal transportation in these fields has been popularized twelve years ago by Rubner et al. for image retrieval and texture classification, with the introduction of the so-called Earth Mover's Distance (EMD). Nowadays, Monge-Kantorovich distances are used for applications as various as object recognition and image registration. The other interesting aspect of this theory lies in the transportation map itself and the possibility to define barycenters between multiple distributions. These notions permit many image and video modifications, such as contrast and color transfer, or texture mixing, to name just a few. However, optimal transport suffers from two important flaws for such applications. First, discrete optimal transport maps are generally irregular and tend to produce artifacts in images. The second drawback is that optimal transport generally leads to computationally expensive solutions, which make it impracticable in many real applications. We will see how these problems can be handled in practice, by introducing well chosen regularization and approximations

Aggregation equations are used to model nonlocal interactions in biology and related problems in which a population density moves with a velocity that depends nonlocally on the density through an aggregation interaction kernel.
The mathematical behavior of these equations has direct connection to problems in optimal transport and incompressible fluid dynamics. I will review recent results for these problems and the role of geometry in the dynamics of both smooth and singular solutions

In this introductory talk we consider logarithmic Sobolev inequalities
(LSI) and their relationship with the Poincare and Talagrand inequalities.
We review the well-known Holley-Stroock and Bakry-Emery conditions for LSI. Finally, we explain the idea behind the two-scale method for LSI (see Grunewald-Otto-Villani-W.). If time permits, we will also discuss the two-scale method for the hydrodynamic limit

In this talk I will present some interpolation inequalities which arise in the study of pattern formation in physics.
In many physical problems described by a variational model (such as domain branching in ferromagnets, superconductors, twin branching in shape memory alloys), the energy is given by the competition of two main terms: an interfacial energy (described by a BV-norm) and a transport term (described by a negative norm or a Wasserstein distance). In order to establish a rigorous lower bound for the energy of minimizing configurations, one needs suitable interpolation inequalities. I will describe the connection between these interpolation estimates and the physical problem, and I will sketch the proof of some of these estimates.
This is a joint work with Felix Otto.

We study finite speed of support propagation and finite-time blow-up of non-negative solutions for the long-wave unstable thin-film equation. We consider a large range of exponents (n,m) within the super-critical m>n+2 and critical m+2 regimes. For the initial data with negative energy we prove that the solution that blows up in finite time satisfies mass concentration phenomena near the blow-up time.
Joint work with:
Mary Pugh, Roman Taranets